Ratio of circumference to diameter of circle

Question

I was reading in a book that ratio of circumference to diameter of a circle is $22:7$ or 3$55:113$.Why is it $355:113$?I can understand $22:7$ but what about $355:113$.Thanks for any help.

Answer 1

Expressing $\pi$ as a ratio of two integers will always only give you an approximation. But the approximation improves if you have larger integers.

Try this. Using your calculator, divide $22$ by $7$. Write down the result. Now, divide $355$ by $113$. Write down the result. Finally, hit the key marked $\pi$ on your calculator. (This is also an approximation, but accurate to several decimal places.) Write that down.

Which ratio is closer to your calculator value of $\pi$? Can you find a closer approximation using a ratio of 4-digit integers?